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Low rank approximation of a matrix (hereafter LRA) is a highly important area of Numerical Linear and Multilinear Algebra and Data Mining and Analysis. One can operate with an LRA at sublinear cost -- by using much fewer memory cells and…
Satisfiability Modulo Theories (SMT) specifications often rely on quantifiers to remain concise and declarative. However, checking the satisfiability of such specifications directly can be inefficient. A common optimization is to ground the…
We provide simple and fast polynomial time approximation schemes (PTASs) for several variants of the max-sum diversification problem which, in its most basic form, is as follows: Given n points p_1,...,p_n in R^d and an integer k, select k…
We present a new algorithm for solving the real roots of a bivariate polynomial system $\Sigma=\{f(x,y),g(x,y)\}$ with a finite number of solutions by using a zero-matching method. The method is based on a lower bound for bivariate…
This paper presents a comprehensive survey of methods which can be utilized to search for solutions to systems of nonlinear equations (SNEs). Our objectives with this survey are to synthesize pertinent literature in this field by presenting…
A matrix algorithm runs at {\em sublinear cost} if it uses much fewer memory cells and arithmetic operations than the input matrix has entries. Such algorithms are indispensable for Big Data Mining and Analysis. Quite typically in that area…
Machine learning algorithms are commonly specified in linear algebra (LA). LA expressions can be rewritten into more efficient forms, by taking advantage of input properties such as sparsity, as well as program properties such as common…
Several new algorithms for deciding emptiness of Boolean combinations of regular languages and of languages of alternating automata (AFA) have been proposed recently, especially in the context of analysing regular expressions and in string…
We study a class of polynomial optimization problems with a robust polynomial matrix inequality (PMI) constraint where the uncertainty set itself is defined also by a PMI. These can be viewed as matrix generalizations of semi-infinite…
We proposes a novel method that enables Graph Neural Networks (GNNs) to solve SAT problems by leveraging a technique developed for applying GNNs to Mixed Integer Linear Programming (MILP). Specifically, k-CNF formulae are mapped into MILP…
Encoding constraints into neural networks is attractive. This paper studies how to introduce the popular positive linear satisfiability to neural networks. We propose the first differentiable satisfiability layer based on an extension of…
This work focuses on improving state-of-the-art in stochastic local search (SLS) for solving Boolean satisfiability (SAT) instances arising from real-world industrial SAT application domains. The recently introduced SLS method CRSat has…
We consider the problem of solving the Min-Sum Submodular Cover problem using local search. The Min-Sum Submodular Cover problem generalizes the NP-complete Min-Sum Set Cover problem, replacing the input set cover instance with a monotone…
The Semi-Implicit Root solver (SIR) is an iterative method for globally convergent solution of systems of nonlinear equations. Since publication, SIR has proven robustness for a great variety of problems. We here present MATLAB and MAPLE…
In this paper, a class of general nonlinear programming problems with inequality and equality constraints is discussed. Firstly, the original problem is transformed into an associated simpler equivalent problem with only inequality…
We study composite optimization problems in which the smooth part of the objective function is \( p \)-times continuously differentiable, where \( p \geq 1 \) is an integer. Higher-order methods are known to be effective for solving such…
Stochastic local search (SLS) algorithms have exhibited great effectiveness in finding models of random instances of the Boolean satisfiability problem (SAT). As one of the most widely known and used SLS algorithm, WalkSAT plays a key role…
Satisfiability Modulo Counting (SMC) encompasses problems that require both symbolic decision-making and statistical reasoning. Its general formulation captures many real-world problems at the intersection of symbolic and statistical…
We provide a theoretical algorithm for checking local optimality and escaping saddles at nondifferentiable points of empirical risks of two-layer ReLU networks. Our algorithm receives any parameter value and returns: local minimum,…
LLM-powered systems require complex multi-step decision-making abilities to solve real-world tasks, yet current planning approaches face a trade-off between the high latency of inference-time search and the limited generalization of…